Problem Statement:
The town of Newton is mapped on a coordinate grid with the origin at City Hall. Evan's house is located at the point \((-5, 7)\), and Billy's house is located at \((-2, 3)\). We need to determine the distance between Evan's house and Billy's house using the
Distance Formula.
Distance Formula:
The formula for the distance \( D \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a coordinate plane is given by:
\[
D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Step-by-Step Solution:
1.
Identify the coordinates:
- Evan's house: \((x_1, y_1) = (-5, 7)\)
- Billy's house: \((x_2, y_2) = (-2, 3)\)
2.
Substitute the coordinates into the Distance Formula:
\[
D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
\[
D = \sqrt{((-2) - (-5))^2 + (3 - 7)^2}
\]
3.
Simplify the expressions inside the parentheses:
- For \(x_2 - x_1\):
\[
-2 - (-5) = -2 + 5 = 3
\]
- For \(y_2 - y_1\):
\[
3 - 7 = -4
\]
4.
Square the results:
- \((x_2 - x_1)^2 = 3^2 = 9\)
- \((y_2 - y_1)^2 = (-4)^2 = 16\)
5.
Add the squared values:
\[
D = \sqrt{9 + 16} = \sqrt{25}
\]
6.
Take the square root:
\[
D = \sqrt{25} = 5
\]
Final Answer:
The distance between Evan's house and Billy's house is \(5\) units.
Correct Option:
\[
\boxed{C}
\]
Parent Tip: Review the logic above to help your child master the concept of distance problems worksheet.
